Explanation Given: x − y = 3 ; ( 4 , ) , ( 0 , ) , ( , 3 ) Approach Used: The rectangular coordinate system consists of two number lines intersecting at the point 0 on each number line. The horizontal number line is called the x -axis and the vertical number line is called the y -axis. Every point in the rectangular coordinate system corresponds to an ordered pair of numbers such as Thus, to find if an ordered pair is a solution of an equation, i. Replaced the variables by the coordinates of the ordered pair. ii. Solve. iii. If the equation is a true statement then the given ordered pair is a solution of the given equation. A linear equation in two variables is an equation that can be written in the form a x + b y = c where a , b , and c are numbers, and a and b are not both 0 . To graph a linear equation in two variables, follow the steps below:- i. If the equation is of form y = a where a is a number, then the graph of y = a is a horizontal line that crosses the y -axis at a and parallel to the x -axis. Else proceed to next step. ii. If the equation is of form x = a where a is a number, then the graph of x = a is a vertical line that crosses the x -axis at a and parallel to the y -axis. Else proceed to next step. iii. Find three ordered pair solutions of the given equation by assuming the x -value or y -value and replacing the x -value or y -value in the given equation. iv. Plot these three ordered pair solutions on the graph. To graph a point, its position is first located on the x -axis, then on the y -axis and the point is finally plotted when this meet. Each ordered pair corresponds to one point in the graph. v. Draw a line through the plotted points. This the graph of the given linear equation. Calculation: Since, the given equation is not of form y = a or x = a . Hence, it is not parallel to x -axis or y -axis. Since, the given ordered pair is a solution of the given equation, it must satisfy the given equation. That is, replacing the variables in the given equation x − y = 3 by the coordinates of the ordered pair ( 4 , ) , we get 4 − y = 3 y = 4 − 3 y = 1 Thus, the first ordered pair solution for the given equation is ( 4 , 1 )

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ISBN: 9780134708799

Author: Martin-Gay, Elayn

Publisher: PEARSON

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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The given ordered pair solutions of each equation x−y=3 and graph it.

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************* ********************************* Q.1) Classify the following statements as a true or false statements: a. If M is a module, then every proper submodule of M is contained in a maximal submodule of M. b. The sum of a finite family of small submodules of a module M is small in M. c. Zz is directly indecomposable. d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M. e. The Z-module has two composition series. Z 6Z f. Zz does not have a composition series. g. Any finitely generated module is a free module. h. If O→A MW→ 0 is short exact sequence then f is epimorphism. i. If f is a homomorphism then f-1 is also a homomorphism. Maximal C≤A if and only if is simple. Sup Q.4) Give an example and explain your claim in each case: Monomorphism not split. b) A finite free module. c) Semisimple module. d) A small submodule A of a module N and a homomorphism op: MN, but (A) is not small in M.

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Chapter 8 Solutions

Prealgebra (hardcover) (8th Edition)

Ch. 8.1 - Prob. 1CC Ch. 8.1 - Prob. 1VRVC Ch. 8.1 - Prob. 2VRVC Ch. 8.1 - Prob. 3VRVC Ch. 8.1 - Prob. 4VRVC Ch. 8.1 - Prob. 5VRVC Ch. 8.1 - Prob. 6VRVC Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E

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The given ordered pair solutions of each equation x − y = 3 and graph it.

Solution Summary: The author explains how the rectangular coordinate system consists of two number lines intersecting at the point 0 on each number line.

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To complete:

The given ordered pair solutions of each equation x−y=3 and graph it.

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Chapter 8 Solutions

The given ordered pair solutions of each equation x − y = 3 and graph it.

Solution Summary: The author explains how the rectangular coordinate system consists of two number lines intersecting at the point 0 on each number line.

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To complete: The given ordered pair solutions of each equation x−y=3 and graph it.

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Chapter 8 Solutions

To complete:

The given ordered pair solutions of each equation x−y=3 and graph it.